This new procedure of financial audit is based on the requirement that the model should be conceived in such a way that it can reflect in a simplified and accurate manner the approached economic reality.procedure of financial audit, dynamic modeling, hyperbola, indices, financial results

Anca Madalina BOGDAN

English

Research Papers in Economics

Informatica Economică, nr. 1 (41)/2007 
 
92 
The Dynamic Modelling as A Financial Audit Procedure 
 
Anca Mădălina BOGDAN 
„Spiru Haret” University, Craiova 
 
This new procedure of financial audit is based on the requirement that the model should be 
conceived in such a way that it can reflect in a simplified and accurate manner the ap-
proached economic reality. 
Key words: procedure of financial audit, dynamic modelling, hyperbola, indices, financial re-
sults. 
 
ntroduction 
Th
unde
e financial auditor’s knowledge and 
rstanding of the approached economic 
segment, the accurate analysis of the rela-
tions between incomes and results, all de-
pending on time other factors, motivate as to 
use the dynamic modelling procedure and in-
clude it among the procedures of financial 
audit. 
The use of the dynamic modelling offers us a 
clear and detailed image of the analyzed rela-
tion. This procedure helps us to identify the 
cyclic on periodical aspects of the studied 
phenomenon and implicitly the period of 
time. 
We shall further make use of a dynamic 
model with the help of which we are deter-
mining the patterns of the income and of the 
financial results in time and also the relation 
between the two variables. Thus we have 
possibility to analyze in details the economic 
evolution. Using traditional methods we can 
obtain incorrect results. 
Thus, the models of economic evolution roles 
emphasize the between the main indices 
/ratios and reveal their transformations con-
cerning the changing of certain variables. 
A very important role of dynamic modelling 
is to establish the best intervals for the main 
financial rations so that the accomplishment 
of economic objectives should not raise any 
problems. 
Actually, the dynamic modelling made ac-
cording to the objective necessities of the fi-
nancial auditor represents the simplified ex-
pression of the phenomenon. 
The dynamic modelling is a modern tech-
nique especially used in the prevision of the 
economic activities of patrimonial entities, 
but, which, in our opinion, can be useful to 
financial auditors as a procedure for informa-
tion processing. The theoretical elements re-
lated to this procedure are numerous, but 
they are not the topic of this research paper 
so we decided to adapt a dynamic model in 
order to use it as a new procedure of financial 
audit. 
I 
 
The dynamic model 
We considered useful dynamic model from 
the economic literature
1 in which the income 
is considered a linear function of assets and 
capitals and financial result varies according 
to the excess of liquidities. 
⎪ ⎩
⎪
⎨
⎧
− =
− =
•
•
). ) , ( (
), (
2
1
M R Y L h R
S I h Y
                                                
 
The function which has as variables the in-
come and financial result, L (Y, R) is exoge-
nously determined by the flow of liquidities 
M. 
In other words, we have used in this model 
all the positions of the balance shut consid-
ered in this way: 
¾ M - The liquidities represent the total as-
sets (from the balance sheets rd.37+38-62); 
¾ S - The capitals represent the total own 
capitals (from the balance sheet rd. 82); 
¾ G - The credits represent the debts, which 
must be paid in more than a year (from the 
balance sheet rd. 58); 
¾ T - The taxes represent the debts, which 
must be paid in less than a year (from the 
balance sheet rd. 47). 
 
1 Tu  N.P.V.  – Dynamical systems,  Ed. Springer – Verlag, 
Berlin, 1993, p. 108. 
 Informatica Economică, nr. 1 (41)/2007 
 
93
The capitals can be written this way: 
  ) ( ) ( G T T Y s S − + − =
¾ T - Represent the credits and the loans on 
the short term, as well as the revenue debts; 
¾ G - Represent the commercial credits and 
debts; 
¾ The constants s is a rate of adjustment 
within the interval (0,2). 
The function of liquidities is writhen as being 
the difference between the demand of trans-
actions and the profit: 
The constant values h1 and h2 which repre-
sent types of speed of adjustment and can be 
considered as unitary h1= h2 = 1. In the case 
that they are different from 1, transforma-
tions of variables can be made so that they 
disappear. 
Replacing all we have mentioned above in 
the first system we will obtain: 
⎪ ⎩
⎪
⎨
⎧
− − =
+ − − − − =
•
•
.
, ) 1 (
M R Y R
G T s R sY Y
β
 
This is a relative dynamic system which de-
pends on two parameters s and β . 
0 1≠ + β s If  ,  a possible situation from the 
economic point of view, the system admits a 
single point of balance: 
[ ]
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
+
− + +
−
+
− + −
=
1
) 1 (
,
1
) 1 (
0
β β
β
s
T s G sM
s
T s G M
u
Analyzing the system: 
⎪ ⎩
⎪
⎨
⎧
− − =
+ − − − − =
•
•
.
, ) 1 (
M R Y R
G T s R sY Y
β
 
we consider that  1 − ≠ s β .  In this situation 
the system admits a single point of balance, 
the solution of the algebraic system: 
⎩
⎨
⎧
= − −
= + − − − −
. 0
, 0 ) 1 (
M R Y
G T s R sY
β
 
which is  
)
1
) 1 (
,
1
) ) 1 ( (
( ) , ( 0 0 +
− + +
−
+
− + −
= =
s
T s G sM
s
T s G M
R y u
β β
β
The system round of this point is:  0 2 : 1 = − − β s d 0 2 : 2 = + − β s d ,   from the 
space of the parameters (red). 
⎪ ⎩
⎪
⎨
⎧
− =
− − =
•
•
.
,
R Y R
R sY Y
β
  The product P is annulled or hyperbola 
(blue).  1 : = β s H
and the associated matrix is   
with the characteristic equation 
, for which the 
sum, respectively the product of the radicals 
are 
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
−
− −
=
β 1
1 s
A
We also have, on the straight line of equation 
0 : = + β s d (green),  , 
which means that here the point of balance is 
unhyperbolic, centre, the system admitting a 
periodical solution. 
0 , 0 , 0 > = < Δ P S
0 1 ) (
2 = + − + + β λ β λ s s
This balance/equilibrium can be stable or un-
stable, the trajectory of phase can be conver-
gent or not. A complete characterization of 
the system is given in the following table. 
) ( 2 1 β λ λ − − = + = s S , 
β λ λ s P − = = 1 2 1 . 
The discriminator of the equation is 
.     
This is annulled when the parameters s and 
) 2 )( 2 ( 4 ) (
2 + − − − = − − = Δ β β β λ s s s
β  go over the straight lines of equations 
Table 1 
Proper values  The type of the point of balance equilib-
rium
 Region 
repulsive  (instable) knot   B  ∈ 2 1,λ λ R ,  0 1> λ ,  0 2> λ  
saddle (instable)   C,  D  ∈ 2 1,λ λ R ,  0 1> λ ,  0 2< λ  
neutral saddle (instable)   3  ∈ 2 1, 0 2 1 = +λ λ λ λ R ,   Informatica Economică, nr. 1 (41)/2007 
 
94 
saddle-knot  (instable)  
β
β λ
1
2 − = 0 > Δ
  2, 4  0 1= λ ,   
repulsive  (instable) knot repulsive  (insta-
ble) knot   G  ∈ 2 1,λ λ R ,  0 1> λ ,  0 2> λ  
 7  double unhyperbolic degenerate  ∈ 2 1,λ λ R ,  0 2 1 = = λ λ  
attractive knot (stable)   E  ∈ 2 1,λ λ R ,  0 1< λ ,  0 2< λ  
1, 8  ∈ 2 1,λ λ R ,  0 2 1 > = λ λ   repulsive degenerate knot (instable)   
0 = Δ ∈ 2 1, attractive degenerate knot (stable) 
  5  λ λ R ,  0 2 1 < = λ λ  
repulsive focus (instable)   A  ∉ 2 1,λ λ R ,  0 Re > λ  
0 < Δ ∉ 2 1, centre (periodical solution)  6  λ λ R ,  0 Re = λ ,  
attractive focus (stable)   F  ∉ 2 1, λ λ R ,    0 Re < λ
 
 
 
 
 
a) Income versus financial result  1 , 2 0 = Y u.m., and final financial results 
b) Income versus financial result versus time  1 , 2 0 = Y u.m., in 1999, the system has on un-
stable behaviour evolving from the equilib-
rium state to a state of explosive variation. 
c) Income versus time 
d) Financial result versus time 
Using a computer program for dynamic sys-
tems we can visualize the evolution of the 
system, varying the parameters and settling 
the initial data. 
5 , 0 = s 5 , 0 − = β   and 2. When  , with initial 
conditions Y 
Thus we consider it useful to further present 
some relevant cases: 
1. For the values of parameters   and  5 , 1 = s
1 = β , considering as on initial data, income 
0 = 6,7 u.m.,   u.m., 
obtained in 2004 when the patrimonial entity 
introduced the International Accounting 
Standards, the system admits a periodical 
situation, being in a continuers state of varia-
tion. 
38 , 1 0 − = RInformatica Economică, nr. 1 (41)/2007 
 
95
Analyzing the situation presented in Figure 2, 
the following aspects can be noticed: 
c) A stage of crisis, of economic depressive 
occurs in the third stage, when both variables 
decrease;  a) In the first stage, both variables increase, 
this leads the entity to prosperity.  d) In the fourth stage the firm is brought to 
an efficient state since incomes increase, but 
the profit decreases (losses occur). 
b) The second stage corresponds to a period 
of saturation when the income decreases, but 
the profit increases; 
 
 
Fig.1. The evolution from the equilibrium/balance to the explosive variation 
 
Fig.2. The periodical orbit with 4 phases/stages 
 
In the next figure, we can notice the evolution of the income in time, and also the financial re-Informatica Economică, nr. 1 (41)/2007 
 
96 
sult, in the considered situation. 
 
Fig.3. The state of continuous variation 
 
a) Income versus financial result  c) Income versus time 
b) Income versus financial result versus time  d) Financial result versus time 
 
 
Fig.4.The system converges to the equilibrium state 
 
3. When   and 5 , 0 = s 1 − = β Further or introducing the numerical results 
is the studied system and using an adequate 
computer programs, the following numerical 
results are obtained. 
, with initial data 
u.m.,  u.m.  in 2005, the 
point of balance of the system in an attractive 
focus, that system is stable, its trajectories 
evolving towards equilibrium point. 
8 , 7 0 = Y 11 , 1 0 − = R
We consider the numerical data correspond-Informatica Economică, nr. 1 (41)/2007 
 
97
ing to 2004. 
¾ G the debits which must be paid in more 
than a year, with the corresponding value to 
2004, G=3,34; 
¾ T the debits which must be paid in less 
than a year with the corresponding value to 
2004, T=5,37; 
¾ M total assets with the corresponding 
value to 2004, M=2,24; 
¾ Y the incomes with the corresponding 
value to 2004,Y(2)=6,7; 
¾ R the financial results with the corre-
sponding value to 2004, R(2)=-1,38. 
Introducing these data in the computer pro-
grams corresponding to the dynamic system, 
we get the following numerical results: 
For 2006, we get the following numerical re-
sults: 
Y(6) =7.527667983899726; 
R(6) =-0.873185592180263. 
For 2007, we get the following numerical re-
sults: 
Y(7) =8.182884604019016; 
R(7) =-0.3153880974491396. 
In 2010, we will have: 
Y(8) =12.59417543721213; 
R(8) = 1.477564799533792. 
  
Conclusions  
The use of the dynamic modelling as a new 
procedure financial audit has the advantage 
of a very well elaborate mathematic system 
studying both the existence and the stability 
of the equilibrium solutions, since a solution 
of instable equilibrium cannot notice in real-
ity. 
In the study of the practical efficiency of this 
procedure we were inspired by the English 
saying: “Time is money”, this presenting 
/reflecting on of the advantages of using this 
method by financial auditors, that is to re-
duce the time of understanding the economic 
and financial situation of their client, as well 
as the obtaining of a useful prevision. 
Another advantage, equally important is the 
fact the new procedure could replace the cal-
culation of all financial and economic ratios, 
a difficult method that requires more time. 
The last and maybe the must important ad-
vantage is that this procedure of dynamic 
modelling, helps us to identify the cyclic on 
periodical aspects of the patrimonial entities 
and implicitly the time which is referred to. 
Still, there is a possible risk to not determine 
the mistakes of accounts. Practically this risk 
is not a disadvantage specific for this proce-
dure, because, on the one hand the calcula-
tion of the economic and financial ratios pre-
sents the same risk and on the other hand us-
ing the other procedures of financial audit as 
well eliminates this risk. 
In the end taking into account all the pre-
sented aspects, we consider that the advan-
tages of using this procedure surpass the pos-
sible disadvantages which encourages us to 
recommend this new method of financial au-
dit and to persuade the financial auditors that 
best results are obtained in short time.  
 
References  
[1] Bogdan, A. M. – The financial audit har-
monized with the International Accounting 
Standards,  Edition Universitaria, Craiova, 
2005. 
[2] Ciurlău, C.; Tomiţă, I. – Macroeconomic 
prevision, Edition Dova, Craiova, 1996. 
[3] Defliese, P.L., Jaemicke,H.R., Sullivan, 
J.D., Gnospelius, R.A.- Montgomery's audit-
ing, New York,1986. 
[4] Holmes, A.W.; Burns, D.C. - Auditing – 
Standards and procedures, Ontario, 1979. 
[5] Raffegeau, J.;Dufils, P.; Lopater, C.; Ar-
faoui, F. - Mémento Pratique Comptable, 
Édition Francis Lefebvre, France,1997. 
[6] Tu  N.P.V.  – Dynamical systems,  Ed. 
Springer – Verlag, Berlin, 1993. 
[7] Ungureanu, L.; Popescu, I.; Comşa, M .- 
Prevision a premise of lasting development, 
vol. II, Edition "România de Mâine", Bucha-
rest, 2003. 
 

Auditing – Standards and procedures,

Mémento Pratique Comptable, Édition Francis Lefebvre,

Montgomery's auditing,

Prevision a premise of lasting development, vol. II, Edition &quot;România de Mâine&quot;,

The financial audit harmonized with the International Accounting Standards, Edition Universitaria,

The Dynamic Modelling as a Financial Audit Procedure

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The Dynamic Modelling as a Financial Audit Procedure

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